Incubation Period and Serial Interval of Mpox in 2022 Global Outbreak Compared with Historical Estimates

Understanding changes in the transmission dynamics of mpox requires comparing recent estimates of key epidemiologic parameters with historical data. We derived historical estimates for the incubation period and serial interval for mpox and contrasted them with pooled estimates from the 2022 outbreak. Our findings show the pooled mean infection-to-onset incubation period was 8.1 days for the 2022 outbreak and 8.2 days historically, indicating the incubation periods remained relatively consistent over time, despite a shift in the major mode of transmission. However, we estimated the onset-to-onset serial interval at 8.7 days using 2022 data, compared with 14.2 days using historical data. Although the reason for this shortening of the serial interval is unclear, it may be because of increased public health interventions or a shift in the mode of transmission. Recognizing such temporal shifts is essential for informed response strategies, and public health measures remain crucial for controlling mpox and similar future outbreaks.

mean incubation period.Finally, a dataset consisting mostly of U.S. mpox cases, collected by Madewell et al. (11), was included in the meta-analysis conducted in this study.

b. Outcome Measures and Study Selection
The outcome variable within each dataset was the mean estimate of the incubation period.
It was measured for all cases within each dataset with information on what day they were exposed to mpox and what day their symptoms began.
For the pre-2022 mpox publications, search results were screened first through titles and abstracts.In this screening stage, publications without full electronic texts available and irrelevant studies were removed.The full texts of the remaining studies were examined and, in the next screening stage, those without the required data-definitive exposure and individual case information-were removed during the screening process.For the global 2022 mpox outbreak studies, new studies were included in the meta-analysis as their data became available.
Then, data extraction was conducted for the remaining articles that made it through the screening process.When available, we aimed to collect data about studies' author names, publication date, and for each individual case ID, sex, age, country of origin, disease exposure and symptom onset date, rash onset date, list of symptoms, testing date, disease confirmation date, source of infection, transmission method, and disease status (i.e., confirmed, probable, or suspected).

c. Data Descriptions and Preparation for Analysis
To meet the inclusion criteria, each case  found in the literature was required to have, at least, partial information on the time window of exposure ( , ,  , ) and the time window of symptom onset � , ,  , �.The following adjustments could be made: • When only the lower boundary of the exposure interval ( , ) was definitive, but the upper boundary ( , ) was unknown or it was later than the upper boundary of the symptom onset interval, we set   to the upper boundary of the symptom onset interval  , , i.e.,  , ≔  , IF  , is known AND ( , is unknown OR  , >  , ); • All symptom onset dates were definitive, implying the respective time interval is of 1-day long ( , ≔  , ).
In total, 42 case records were aggregated, including 38 records with completely observed exposure time interval, and 4 records which were censored.
Similar data preparation techniques were applied to estimate the mean exposure-to-rash incubation period, resulting in 20 case records, including 4 censored records.
d. Assessing the Retrieved Datasets Among all of the currently available mpox incubation period estimates, the present study focused on studies reporting the distribution of incubation periods along with the mean and 95% CrI of that distribution for the hierarchical meta-analyses.Then, the present study created incubation period distributions for datasets where they had not yet been estimated or where estimates could be further improved (e.g., by adjusting for right truncation).May through 29 June 2022.The authors collected participant data by conducting interviews using a standard case report form and offered lesion, anal, and oropharynx swabs for RT-PCR testing.In addition to collecting data on date of infection and symptom onset, they also collected data on rash onset dates.

Viedma-Martinez et al. (38) Data
Identification of case transmission data of mpox from an outbreak rooted in a tattoo parlor in Cadiz, Spain resulted in 21 confirmed reported cases of mpox, all of whom had visited the tattoo parlor around the same couple of weeks.Most of the cases visited the parlor to get a piercing except for one, who got a tattoo only.To extract and synthesize data for the dates of exposure and dates of symptom onset, we retrieved all available information from the relevant sources.

Miura et al. (7) Data
These data were collected from an outbreak of mpox in the Netherlands and had exact dates of exposure for 13 out of 18 cases, and the exact dates of symptom onset for all cases.
Where exposure date was uncertain, a range of dates was available, with a left margin and a right margin.

Guzzetta et al. (8) Data
An outbreak of confirmed mpox cases in Italy through 8 July 2022 contained complete information (i.e., a known date of exposure and symptom onset) for 15 individual cases.When exposure date was uncertain, a range of earliest exposure and latest exposure was available, for a total of 18 cases included in this study.

B. Statistical Analysis
a. Bayesian Framework Time interval distributions were estimated using Markov chain Monte Carlo (MCMC) sampling techniques for each available dataset.Subsequently, a meta-analysis was conducted by pooling the time interval estimates reported in the literature, along with the estimated values obtained from the present study's analysis, and employing a Bayesian hierarchical/partial pooling model.Bayesian estimation was implemented using Stan software (https://mc-stan.org).
Each run of simulations was consistent of 4 parallel chains with 15,000 posterior draws including 2,500 draws used for tuning-in and disregarded for the final output.Code scripts and all supporting information are publicly available and can be accessed on designated repository: https://github.com/aakhmetz/Mpox-IncubationPeriodSerialInterval-Meta2023

b. Time Interval Estimation
This study involved multiple datasets, each containing information on exposure dates, symptom onset dates, and rash onset dates.Censored data was handled by assigning a weakly informative prior distribution.Then, data lists were constructed for each dataset and descriptively named, including the number of observations (), exposure dates' lower boundaries,   , symptom or rash onset dates' lower boundaries,   , and corresponding upper boundaries of these dates,   and   , when available.The same framework was adapted for transmission (infectorinfectee) pairs data set, with the only difference being that the exposure dates,   and   , would stand for the onset dates of the infector, and onset dates,   and   , would stand for the onset dates of the infectee.
For situations where data were missing, the data lists included censored and observed counterparts, such as censored case observations,   , complete case observations,   ( =   +   ), censored lower boundary of the exposure,  , =  , , and observed ones,  , =  , , with the defined prior: The time of exposure,   , and the time of symptom onset,   , were then assumed to be uniformly distributed within their respective intervals: ~ Uniform(lower =  , , upper =  , + 1)   ~ Uniform(lower =  , , upper =  , + 1) where  = 1, … , .
Each time interval (infection-to-onset and infection-to-rash incubation periods, as well as onset-to-onset and rash-to-rash serial intervals) were fitted to the data using five different models-one of three (gamma, Weibull, or lognormal) distributions, their mixture within a Bayesian mixture model, and the generalized gamma distribution (GGD).
In case of using individual distributions  (gamma, Weibull, lognormal, or GGD;  = 1, 2, 3, 4, respectively), the likelihood was a product of probability density functions,   ( − ; ), at each interval   −   , given by: The   was defined by a set of parameters , including the mean, , and SD, .All In case of the Bayesian mixture model, the overall likelihood, , was given by a mixture of three component likelihoods with respective weights   : These weights were then estimated as part of the fitting process.To facilitate algorithm convergence, two parameters, the mean and standard deviation (SD), were assigned to be common to all three distributions (49).
The posterior probability for selecting the distribution  is defined by the expression: In case of analyzing the rash-to-rash serial interval, the cut-off value, , was imposed, when all data points with intervals below  were truncated.This led to a left-truncated likelihood modified from the form (1): where  � (∘; ) = 1 − (∘; ) is a complimentary cumulative distribution function.

C. Sensitivity Analysis for Rash-To-Rash Serial Interval
In addition to the eight-day cut-off value considered for Appendix Figure 1B, we also calculated the rash-to-rash serial interval under alternative conditions.First, varying the cut-off value between 2 and 10 days yielded a mean rash-to-rash serial interval ranging from 11.9 days to 15.0 days (95% CrI 10.7-16.0days).Second, we modeled the rash-to-rash interval data using a composition of two distributions: the exponential or scaled standard normal distribution and the serial interval distribution.Both the exponential distribution and the scaled normal distribution as the first component yielded a mean serial interval of 15.1 days (95% CrI 14.2-16.0days).

Table 1 .
Consistency in case definition of symptom onset across different studies

Table 2 .
Infection-to-onset incubation period in studies of mpox before the 2022 outbreak and in the 2022 outbreak* The studies are ordered by their publication dates.Mean and SD are represented by their posterior means and 95% CrI; median and range are represented only by their posterior means.ICC, interval censoring corrected model; ICRTC, interval censoring and right truncation corrected model; Range, 95% CrI as the interval between 2.5th and 97.5th percentiles of the posterior distribution; n/a, not available as it was not stated in the original study. *

Table 3 .
Infection-to-rash incubation period in studies of mpox before the 2022 outbreak and in the 2022 outbreak* The studies are ordered by their publication dates.Mean and SD are represented by their posterior means and 95% CrI; median and range are represented only by their posterior means.ICC, interval censoring corrected model; ICRTC, interval censoring and right truncation corrected model; Range, 95% CrI as the interval between 2.5th and 97.5th percentiles of the posterior distribution; n/a, not available as it was not stated in the original study. *